ESTADISTICA PARA EL ANALISIS POLITICO II

Análisis Factorial I: Exploración

Hacemos analisis factorial para reducir las variables en otras variables resumen. Mientras la clusterización agrupaba filas, la factorización agrupa columnas. Pero, al igual que en clusterización, queremos saber si las nuevas variables tienen un nombre, al cual se le denomina técnicamente variable latente. En esta sesión exploraremos la data a ver qué emerge.

Preparación de Datos:

Para esta sesión trabajaremos con la data de estos links:

Veamos que tenemos:

str(demo)
## 'data.frame':    167 obs. of  10 variables:
##  $ Rank                    : chr  "1" "2" "3" "4" ...
##  $ Country                 : chr  "Norway" "Iceland" "Sweden" "New Zealand" ...
##  $ Score                   : chr  "9.87" "9.58" "9.39" "9.26" ...
##  $ Elec­toral              : chr  "10.00" "10.00" "9.58" "10.00" ...
##  $ Functio­ning            : chr  "9.64" "9.29" "9.64" "9.29" ...
##  $ Poli­ticalpartici­pation: chr  "10.00" "8.89" "8.33" "8.89" ...
##  $ Poli­ticalculture       : chr  "10.00" "10.00" "10.00" "8.13" ...
##  $ Civilliber­ties         : chr  "9.71" "9.71" "9.41" "10.00" ...
##  $ Regimetype              : chr  "Full democracy" "Full democracy" "Full democracy" "Full democracy" ...
##  $ Conti­nent              : chr  "Europe" "Europe" "Europe" "Oceania" ...
str(happy)
## 'data.frame':    156 obs. of  9 variables:
##  $ Overall    : chr  "1" "2" "3" "4" ...
##  $ Country    : chr  "Finland" "Norway" "Denmark" "Iceland" ...
##  $ Score      : chr  "7.632" "7.594" "7.555" "7.495" ...
##  $ GDP        : chr  "1.305" "1.456" "1.351" "1.343" ...
##  $ Social     : chr  "1.592" "1.582" "1.590" "1.644" ...
##  $ Healthy    : chr  "0.874" "0.861" "0.868" "0.914" ...
##  $ Freedom    : chr  "0.681" "0.686" "0.683" "0.677" ...
##  $ Generosity : chr  "0.202" "0.286" "0.284" "0.353" ...
##  $ Perceptions: chr  "0.393" "0.340" "0.408" "0.138" ...

Eliminemos columnas que no usaremos esta vez:

happy$Overall=NULL
demo[,c(1,9,10)]=NULL

También debemos tener nombres diferentes en los scores antes del merge:

names(happy)[names(happy)=="Score"]="ScoreHappy" 
names(demo)[names(demo)=="Score"]="ScoreDemo"

Tenemos:

str(demo)
## 'data.frame':    167 obs. of  7 variables:
##  $ Country                 : chr  "Norway" "Iceland" "Sweden" "New Zealand" ...
##  $ ScoreDemo               : chr  "9.87" "9.58" "9.39" "9.26" ...
##  $ Elec­toral              : chr  "10.00" "10.00" "9.58" "10.00" ...
##  $ Functio­ning            : chr  "9.64" "9.29" "9.64" "9.29" ...
##  $ Poli­ticalpartici­pation: chr  "10.00" "8.89" "8.33" "8.89" ...
##  $ Poli­ticalculture       : chr  "10.00" "10.00" "10.00" "8.13" ...
##  $ Civilliber­ties         : chr  "9.71" "9.71" "9.41" "10.00" ...
str(happy)
## 'data.frame':    156 obs. of  8 variables:
##  $ Country    : chr  "Finland" "Norway" "Denmark" "Iceland" ...
##  $ ScoreHappy : chr  "7.632" "7.594" "7.555" "7.495" ...
##  $ GDP        : chr  "1.305" "1.456" "1.351" "1.343" ...
##  $ Social     : chr  "1.592" "1.582" "1.590" "1.644" ...
##  $ Healthy    : chr  "0.874" "0.861" "0.868" "0.914" ...
##  $ Freedom    : chr  "0.681" "0.686" "0.683" "0.677" ...
##  $ Generosity : chr  "0.202" "0.286" "0.284" "0.353" ...
##  $ Perceptions: chr  "0.393" "0.340" "0.408" "0.138" ...

Y ahora arreglemos el tipo de variables:

demo[,-c(1)]=lapply(demo[,-c(1)],as.numeric)
happy[,-c(1)]=lapply(happy[,-c(1)],as.numeric)
## Warning in lapply(happy[, -c(1)], as.numeric): NAs introduced by coercion

Eliminemos al perdidos al perdido:

happy=na.omit(happy)

** Presta atención al merge**. Usualmente hacemos merge por default y luego perdemos varias filas:

nrow(merge(happy,demo))
## [1] 145

Hagamos un nuevo merge, donde veamos TODO:

HappyDemo=merge(happy,demo,all.x=T, all.y=T)

Esta vez HappyDemo tiene varios paises de más, pero con valores perdidos y nombres que no pudieron coincidir. Veamos:

HappyDemo[!complete.cases(HappyDemo),]
##                              Country ScoreHappy   GDP Social Healthy
## 14                            Belize      5.956 0.807  1.101   0.474
## 27                        Cape Verde         NA    NA     NA      NA
## 33                           Comoros         NA    NA     NA      NA
## 34               Congo (Brazzaville)      4.559 0.682  0.811   0.343
## 35                  Congo (Kinshasa)      4.245 0.069  1.136   0.204
## 38                              Cuba         NA    NA     NA      NA
## 41  Democratic Republic of the Congo         NA    NA     NA      NA
## 43                          Djibouti         NA    NA     NA      NA
## 48                 Equatorial Guinea         NA    NA     NA      NA
## 49                           Eritrea         NA    NA     NA      NA
## 51                          Eswatini         NA    NA     NA      NA
## 53                              Fiji         NA    NA     NA      NA
## 57                            Gambia         NA    NA     NA      NA
## 64                     Guinea-Bissau         NA    NA     NA      NA
## 65                            Guyana         NA    NA     NA      NA
## 84                            Kosovo      5.662 0.855  1.230   0.578
## 95                         Macedonia      5.185 0.959  1.239   0.691
## 117                      North Korea         NA    NA     NA      NA
## 118                  North Macedonia         NA    NA     NA      NA
## 119                  Northern Cyprus      5.835 1.229  1.211   0.909
## 121                             Oman         NA    NA     NA      NA
## 123                        Palestine         NA    NA     NA      NA
## 124          Palestinian Territories      4.743 0.642  1.217   0.602
## 126                 Papua New Guinea         NA    NA     NA      NA
## 133            Republic of the Congo         NA    NA     NA      NA
## 144                          Somalia      4.982 0.000  0.712   0.115
## 147                      South Sudan      3.254 0.337  0.608   0.177
## 151                         Suriname         NA    NA     NA      NA
## 159                      Timor-Leste         NA    NA     NA      NA
## 161                Trinidad & Tobago      6.192 1.223  1.492   0.564
## 162              Trinidad and Tobago         NA    NA     NA      NA
## 168             United Arab Emirates         NA    NA     NA      NA
##     Freedom Generosity Perceptions ScoreDemo Elec­toral Functio­ning
## 14    0.593      0.183       0.089        NA         NA           NA
## 27       NA         NA          NA      7.88       9.17         7.86
## 33       NA         NA          NA      3.71       4.33         2.21
## 34    0.514      0.091       0.077        NA         NA           NA
## 35    0.312      0.197       0.052        NA         NA           NA
## 38       NA         NA          NA      3.00       1.08         3.57
## 41       NA         NA          NA      1.49       0.50         0.71
## 43       NA         NA          NA      2.87       0.42         1.79
## 48       NA         NA          NA      1.92       0.00         0.43
## 49       NA         NA          NA      2.37       0.00         2.14
## 51       NA         NA          NA      3.03       0.92         2.86
## 53       NA         NA          NA      5.85       6.58         5.36
## 57       NA         NA          NA      4.31       4.48         4.29
## 64       NA         NA          NA      1.98       1.67         0.00
## 65       NA         NA          NA      6.67       9.17         5.71
## 84    0.448      0.274       0.023        NA         NA           NA
## 95    0.394      0.173       0.052        NA         NA           NA
## 117      NA         NA          NA      1.08       0.00         2.50
## 118      NA         NA          NA      5.87       6.50         5.36
## 119   0.495      0.179       0.154        NA         NA           NA
## 121      NA         NA          NA      3.04       0.00         3.93
## 123      NA         NA          NA      4.39       3.83         2.14
## 124   0.266      0.086       0.076        NA         NA           NA
## 126      NA         NA          NA      6.03       6.92         6.07
## 133      NA         NA          NA      3.31       3.17         2.50
## 144   0.674      0.238       0.282        NA         NA           NA
## 147   0.112      0.224       0.106        NA         NA           NA
## 151      NA         NA          NA      6.98       9.17         6.43
## 159      NA         NA          NA      7.19       9.08         6.79
## 161   0.575      0.171       0.019        NA         NA           NA
## 162      NA         NA          NA      7.16       9.58         7.14
## 168      NA         NA          NA      2.76       0.00         3.93
##     Poli­ticalpartici­pation Poli­ticalculture Civilliber­ties
## 14                        NA                NA              NA
## 27                      6.67              6.88            8.82
## 33                      4.44              3.75            3.82
## 34                        NA                NA              NA
## 35                        NA                NA              NA
## 38                      3.33              4.38            2.65
## 41                      2.22              3.13            0.88
## 43                      3.89              5.63            2.65
## 48                      3.33              4.38            1.47
## 49                      1.67              6.88            1.18
## 51                      2.22              5.63            3.53
## 53                      6.11              5.63            5.59
## 57                      3.33              5.63            3.82
## 64                      2.78              3.13            2.35
## 65                      6.11              5.00            7.35
## 84                        NA                NA              NA
## 95                        NA                NA              NA
## 117                     1.67              1.25            0.00
## 118                     6.67              3.75            7.06
## 119                       NA                NA              NA
## 121                     2.78              4.38            4.12
## 123                     7.78              4.38            3.82
## 124                       NA                NA              NA
## 126                     3.89              5.63            7.65
## 133                     3.89              3.75            3.24
## 144                       NA                NA              NA
## 147                       NA                NA              NA
## 151                     6.67              5.00            7.65
## 159                     5.56              6.88            7.65
## 161                       NA                NA              NA
## 162                     6.11              5.63            7.35
## 168                     2.22              5.00            2.65

De lo anterior date cuenta que, por un lado, hay paises que les falta un bloque de indicadores, y que en muchos casos los nombres están mal escritos. Podemos recuperar algunos, pero su data original:

# cambiemos a nombres mas sencillos:
## en demo
demo[demo$Country=="Democratic Republic of the Congo",'Country']="Congo (Kinshasa)"
demo[demo$Country=="Republic of the Congo",'Country']="Congo (Brazzaville)"
demo[demo$Country=="Trinidad and Tobago",'Country']="Trinidad & Tobago"
demo[demo$Country=="North Macedonia",'Country']="Macedonia"

## en happy
happy[happy$Country=="Palestinian Territories",'Country']="Palestine"

Luego de esos ajustes veamos:

HappyDemo=merge(happy,demo) # re creando HappyDemo
nrow(HappyDemo)
## [1] 150

En efecto se recuperaron 5 paises, asi quedará.

Evaluando data

El análisis factorial requiere que hagamos algunas observaciones previas.

  1. Calculemos matriz de correlación:
theData=HappyDemo[,-c(1,2,9)] # sin los Scores ni nombre de país.

# esta es:
library(polycor)
corMatrix=polycor::hetcor(theData)$correlations
  1. Explorar correlaciones:
library(ggcorrplot)
## Loading required package: ggplot2
ggcorrplot(corMatrix)

ggcorrplot(corMatrix,
          p.mat = cor_pmat(corMatrix),
          insig = "blank")

  1. Verificar si datos permiten factorizar:
library(psych)
## 
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
## The following object is masked from 'package:polycor':
## 
##     polyserial
psych::KMO(corMatrix) 
## Kaiser-Meyer-Olkin factor adequacy
## Call: psych::KMO(r = corMatrix)
## Overall MSA =  0.87
## MSA for each item = 
##                      GDP                   Social                  Healthy 
##                     0.82                     0.92                     0.87 
##                  Freedom               Generosity              Perceptions 
##                     0.86                     0.62                     0.80 
##               Elec­toral             Functio­ning Poli­ticalpartici­pation 
##                     0.81                     0.92                     0.95 
##        Poli­ticalculture          Civilliber­ties 
##                     0.89                     0.84
  1. Verificar si la matriz de correlaciones es adecuada
cortest.bartlett(corMatrix,n=nrow(theData))$p.value>0.05
## [1] FALSE
library(matrixcalc)

is.singular.matrix(corMatrix)
## [1] FALSE
  1. Determinar en cuantos factores o variables latentes podríamos redimensionar la data:
fa.parallel(theData,fm = 'ML', fa = 'fa')

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA

Se sugieren 3, veamos.

  1. Redimensionar a numero menor de factores
library(GPArotation)
resfa <- fa(theData,nfactors = 3,cor = 'mixed',rotate = "varimax",fm="minres")
## 
## mixed.cor is deprecated, please use mixedCor.
print(resfa$loadings)
## 
## Loadings:
##                          MR1    MR3    MR2   
## GDP                       0.268  0.927  0.126
## Social                    0.321  0.663  0.152
## Healthy                   0.345  0.803  0.153
## Freedom                   0.255  0.284  0.516
## Generosity                              0.612
## Perceptions                      0.266  0.683
## Elec­toral                0.935  0.179       
## Functio­ning              0.753  0.429  0.356
## Poli­ticalpartici­pation  0.696  0.341  0.148
## Poli­ticalculture         0.520  0.304  0.507
## Civilliber­ties           0.919  0.317       
## 
##                  MR1   MR3   MR2
## SS loadings    3.404 2.629 1.582
## Proportion Var 0.309 0.239 0.144
## Cumulative Var 0.309 0.548 0.692
print(resfa$loadings,cutoff = 0.51)
## 
## Loadings:
##                          MR1    MR3    MR2   
## GDP                              0.927       
## Social                           0.663       
## Healthy                          0.803       
## Freedom                                 0.516
## Generosity                              0.612
## Perceptions                             0.683
## Elec­toral                0.935              
## Functio­ning              0.753              
## Poli­ticalpartici­pation  0.696              
## Poli­ticalculture         0.520              
## Civilliber­ties           0.919              
## 
##                  MR1   MR3   MR2
## SS loadings    3.404 2.629 1.582
## Proportion Var 0.309 0.239 0.144
## Cumulative Var 0.309 0.548 0.692

Cuando logramos que cada variable se vaya a un factor, tenemos una estructura simple.

fa.diagram(resfa)

  1. Evaluando Resultado obtenido:
summary(resfa)
## 
## Factor analysis with Call: fa(r = theData, nfactors = 3, rotate = "varimax", fm = "minres", 
##     cor = "mixed")
## 
## Test of the hypothesis that 3 factors are sufficient.
## The degrees of freedom for the model is 25  and the objective function was  0.33 
## The number of observations was  150  with Chi Square =  46.53  with prob <  0.0056 
## 
## The root mean square of the residuals (RMSA) is  0.02 
## The df corrected root mean square of the residuals is  0.04 
## 
## Tucker Lewis Index of factoring reliability =  0.961
## RMSEA index =  0.08  and the 10 % confidence intervals are  0.041 0.11
## BIC =  -78.74
resfa$crms
## [1] 0.03691667
resfa$RMSEA
##      RMSEA      lower      upper confidence 
## 0.07968360 0.04056531 0.10959050 0.90000000
resfa$TLI
## [1] 0.9614123
  1. Posibles valores proyectados:

¿Qué nombres les darías?

as.data.frame(resfa$scores)
##             MR1          MR3          MR2
## 1   -0.44581478 -1.368481159 -1.098638556
## 2    0.48033887  0.090566181 -0.856703304
## 3   -1.00967021  0.585592494 -0.898629955
## 4   -1.01725350 -0.201269389 -0.687036544
## 5    0.73624548  0.463261056 -0.807836146
## 6    0.01584794 -0.013422423 -1.259526261
## 7    1.17998664  0.708063729  1.622400763
## 8    0.82303951  0.935375820  0.642938605
## 9   -1.50616013  0.826948485 -0.466857259
## 10  -2.01760261  1.621600785  0.247169356
## 11   0.21131821 -1.001237965  0.199771946
## 12  -1.66996548  0.917390607  0.039008363
## 13   0.79578389  0.823135593  0.752042977
## 14   0.45082762 -1.668920643  0.253673440
## 15  -0.05641176 -0.551594725  0.972541028
## 16   0.50412428 -0.397523850 -0.646284689
## 17   0.08318741  0.219130546 -1.327515737
## 18   1.06057976 -0.053434870 -0.211901993
## 19   0.92310546  0.142136942 -0.826976916
## 20   0.86850458  0.416442028 -1.244491103
## 21   0.06960676 -1.591645737  0.393753312
## 22  -1.01989359 -1.843388059 -0.236504917
## 23  -1.06874704 -0.634535152  1.193457361
## 24  -0.96478982 -0.850195652 -0.051683999
## 25   1.16412448  0.699895023  1.674473964
## 26  -0.82185506 -2.292555222 -0.715561120
## 27  -1.21459683 -1.193530366 -0.601933540
## 28   1.12549099  0.310091463  0.169110288
## 29  -2.02015893  0.930753211  0.730951312
## 30   0.92382717  0.031278951 -0.555349193
## 31  -0.99341039 -0.342515557 -0.440808189
## 32  -1.34392495 -1.731710198 -0.056671606
## 33   1.11687607  0.157292047  0.196185885
## 34   0.53162832  0.480393287 -0.921160352
## 35   0.85011409  0.764563718 -0.554786856
## 36   0.79624528  0.870222852 -0.688471459
## 37   0.94143175  0.714511451  2.121511960
## 38   0.54715397  0.139014157 -0.484753176
## 39   0.50703962 -0.003093982 -0.455381011
## 40  -1.06527183  0.235186366 -0.574312978
## 41   0.68842805 -0.254455499 -1.153543849
## 42   0.89257410  0.571923939  0.195893974
## 43  -1.11306931 -1.184726903  1.091758194
## 44   1.10985513  0.659666822  1.653651197
## 45   0.81540073  0.946585860 -0.223836118
## 46  -1.16044066  0.678685564 -0.957969601
## 47   0.07691544 -0.182138682 -0.664590958
## 48   1.00677308  0.796534944  1.072782633
## 49   0.57933687 -1.062947130  0.102809649
## 50   0.94020552  0.630579743 -1.527306759
## 51   0.39726736 -0.347429130 -0.255826679
## 52  -0.78707349 -1.305764808 -0.336231492
## 53   0.46456787 -1.864571231  0.146446067
## 54   0.55857179 -0.779649140 -0.409560785
## 55  -0.17346845  1.441868311  1.010220747
## 56   0.47287912  0.678256215 -1.060140370
## 57   1.10939209  0.852767876  1.372869501
## 58   0.88601738 -0.785000631  0.101840109
## 59   0.11795711 -0.206917896  0.927890206
## 60  -2.04168760  0.889625721  0.361186027
## 61  -0.95035625  0.548246073 -1.155387122
## 62   0.98365854  1.030709219  1.423727390
## 63   0.11396222  0.866304691  1.406808120
## 64   0.79327364  0.975072334 -0.956233635
## 65  -0.44161397 -1.077594626  0.006215688
## 66   1.04591371 -0.277244425 -0.267832175
## 67   0.76222476  1.001900825  0.153818849
## 68  -0.87467550  0.112047320  0.109949230
## 69  -1.65050509  1.197143904 -0.274185318
## 70  -0.33522854 -0.966870000  1.027485617
## 71  -1.49516709  1.803872673 -0.233903317
## 72   0.04293901 -0.757298467 -0.217984352
## 73  -1.78599653 -0.152032970  0.993701862
## 74   0.97925834  0.456397863 -0.826556978
## 75  -0.77804159  0.538112456 -0.078162481
## 76   0.94805064 -1.522705964 -0.195547331
## 77   0.63831210 -2.262436649 -0.239690918
## 78  -1.68409623  0.712425727 -0.388757551
## 79   1.04840427  0.693005613 -1.315279845
## 80   0.88865588  1.352624510  1.111733995
## 81   0.34657638  0.238754003 -0.733574453
## 82   0.23975441 -1.637992753 -0.252933264
## 83   0.50924510 -2.077682623  0.466171447
## 84   0.15039097  0.505948071  0.394348464
## 85   0.63440877 -1.617044211 -0.370645384
## 86   0.80740644  0.684542762  1.164305786
## 87  -0.34912495 -0.757095434 -0.595649455
## 88   1.11202349  0.179626701  0.506248330
## 89   0.27914706  0.459796315 -0.816176737
## 90   0.69514799 -0.572741827 -0.979962610
## 91   0.71917670 -0.125566004 -0.508518883
## 92   0.21186259  0.422573984 -0.813437625
## 93  -0.45635583 -0.087937715 -0.294497203
## 94  -0.48561718 -1.783217143  0.597131853
## 95  -1.14335379 -0.633287427  1.952906573
## 96   0.45215981 -0.099779520 -0.482248625
## 97   0.08717409 -1.151560004  0.852537682
## 98   0.92601217  0.806327162  1.601247115
## 99   1.26762633  0.471511002  2.002009591
## 100 -0.86360371 -0.173889833  0.193001205
## 101  0.06111228 -2.017396366 -0.389845399
## 102 -0.19638111 -0.770587015 -0.303260964
## 103  1.02148715  1.006708243  1.940850302
## 104 -0.03154804 -0.807150396 -0.230102465
## 105 -0.61081426 -0.232953321 -0.754153058
## 106  0.73062487  0.520443632 -0.681617305
## 107  0.73511658 -0.235024164 -0.469515639
## 108  0.70482067  0.052501923 -0.874432123
## 109  0.72297250 -0.435483094 -0.288170577
## 110  0.58322251  0.726880192 -0.870804685
## 111  0.99402547  0.733652385 -0.644937904
## 112 -2.01905922  2.325144966  0.630535581
## 113  0.60145626  0.544545448 -1.211233623
## 114 -1.42279012  1.248943430 -1.411789904
## 115 -0.90602330 -1.468904392  2.288749138
## 116 -2.34549497  1.837085556 -0.350236398
## 117  0.72638640 -1.398205292  0.210006801
## 118  0.63755954  0.175566272 -0.960254960
## 119  0.29100869 -2.006041810 -0.228120837
## 120 -0.34592659  1.610737584  1.856898063
## 121  0.77684080  0.735887414 -0.978620151
## 122  0.71862466  0.806359213 -0.351334507
## 123  0.74986983 -0.082771999 -0.229027439
## 124  0.81387127  0.840110174 -0.338026089
## 125  0.86650955  0.917892294 -0.285121513
## 126  0.22068499 -0.020427117  0.300412916
## 127 -1.62467476 -0.371226704 -0.280898781
## 128  0.96997873  0.743436655  2.178871590
## 129  0.83345428  0.976979664  1.818733107
## 130 -2.13333912 -0.226400585  0.188606775
## 131  0.97446367  1.032129797 -0.543468218
## 132 -1.78808895 -0.477977648  0.094151298
## 133  0.07830330 -1.310118791  0.599597342
## 134 -0.56502405  0.585696732  0.289474776
## 135 -0.72763414 -1.559224420 -0.121188819
## 136  0.55815746  0.651184758 -0.440521935
## 137  0.09861209  0.105761486 -0.500902501
## 138 -1.22517536  0.961002640 -0.129505220
## 139 -2.31866025  0.943419620 -0.265098142
## 140  0.27386398 -1.633603584  0.420051497
## 141  0.20270976 -0.139502857 -0.874216960
## 142  1.00880031  0.718322029  0.184231055
## 143  0.57524211  1.092845257  0.369168539
## 144  1.29100183  0.219300594  0.406160014
## 145 -2.06860237  0.048333426  1.589742380
## 146 -1.20739186  0.817518450 -1.210069407
## 147 -1.55297428  0.174837293  0.656505739
## 148 -1.75630380 -0.618763549 -0.421561741
## 149  0.34238324 -1.098811528  0.358161254
## 150 -1.01759077 -1.082303889  0.303390169
HappyDemoFA=cbind(HappyDemo[1],as.data.frame(resfa$scores))

library(plotly)
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
plot_ly(data=HappyDemoFA, x = ~MR1, y = ~MR2, z = ~MR3, text=~Country) %>%
  add_markers() %>%
  layout(scene = list(xaxis = list(title = 'Demo'),
                     yaxis = list(title = 'Tranquilidad'),
                     zaxis = list(title = 'Bienestar')))

RECORDANDO:

library(fpc)
library(cluster)
library(dbscan)
## 
## Attaching package: 'dbscan'
## The following object is masked from 'package:fpc':
## 
##     dbscan
# YA NO NECESITAS CMD para HappyDemoFA[,c(2:4)]

g.dist.cmd = daisy(HappyDemoFA[,c(2:4)], metric = 'euclidean')
kNNdistplot(g.dist.cmd, k=3)

Para tener una idea de cada quien:

resDB=fpc::dbscan(g.dist.cmd, eps=0.6, MinPts=3,method = 'dist')
HappyDemoFA$clustDB=as.factor(resDB$cluster)
aggregate(cbind(MR1, MR2,MR3) # dependientes
          ~ clustDB, # nivel
          data = HappyDemoFA,    # data
          max)            # operacion
##   clustDB        MR1        MR2        MR3
## 1       0  0.2206850  2.2887491  2.3251450
## 2       1  1.2910018  2.1788716  1.3526245
## 3       2 -0.4563558 -0.2944972  1.2489434
## 4       3 -1.2251754  0.7309513  1.1971439
## 5       4 -0.5650241  0.2894748  0.5856967
## 6       5 -1.6246748  0.1886068 -0.2264006
plot_ly(data=HappyDemoFA, x = ~MR1, y = ~MR2, z = ~MR3, text=~Country, color = ~clustDB) %>%
  add_markers() %>%
  layout(scene = list(xaxis = list(title = 'Demo'),
                     yaxis = list(title = 'Tranquilidad'),
                     zaxis = list(title = 'Bienestar')))


al INICIO

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